In this work, we propose a projection-free conditional gradient-type algorithm that achieves level-independent oracle complexities (i.e., the dependence of the complexities on the target accuracy is independent of \(T\) ) using only one sample of \((\xi _i)_{1\le i \le T}\)  in each iteration, thereby addressing both of the above challenges. Our algorithm uses moving-average based stochastic estimators of the gradient and function values, also used recently by [1]} and [2]}, along with an inexact conditional gradient method used by [3]} (which in turn is inspired by the sliding method by [4]}). In order to establish our oracle complexity results, we use a novel merit function based convergence analysis. To the best of our knowledge, such an analysis technique is used for the first time in the context of analyzing stochastic conditional gradient-type algorithms.
